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The purpose of this paper is to focus on modeling buoyancy driven viscous flow and heat transfer through saturated packed pebble‐beds via a set of homogeneous volume‐averaged conservation equations in which local thermal disequilibrium is accounted for.

The local thermal disequilibrium accounted for refers to the solid and liquid phases differing in temperature in a volume‐averaged sense, which is modeled by describing each phase with its own governing equation. The partial differential equations are discretized and solved via a vertex‐centered edge‐based dual‐mesh finite volume algorithm. A compact stencil is used for viscous terms, as this offers improved accuracy compared to the standard finite volume formulation. A locally preconditioned artificial compressibility solution strategy is employed to deal with pressure incompressibility, whilst stabilisation is achieved via a scalar‐valued artificial dissipation scheme.

The developed technology is demonstrated via the solution of natural convective flow inside a heated porous axisymmetric cavity. Predicted results were in general within 10 per cent of experimental measurements.

This is the first instance in which both artificial compressibility and artificial dissipation is employed to model flow through saturated porous materials.

The purpose of this paper is to present two low diffusive convective-pressure flux split finite volume algorithms for solving incompressible flows in artificial compressibility framework.

The present method follows the framework similar to advection upwind splitting method of Liou and Steffen for compressible flows which is used by Vierendeels et al. to solve incompressible flow equations. Instead of discretizing the total inviscid flux using upwind scheme, the inviscid flux is first split into convective and pressure parts, and then discretized the two parts differently. The convective part is discretized using upwind method and the pressure part using central differencing. Since the Vierendeels type scheme may not be able to capture the divergence free velocity field due to the presence of artificial dissipation term, a strategy to progressively withdraw the dissipation with time step is proposed here that can ascertain the divergence free velocity condition to the level of residual error. This approach helps in reducing the amount of numerical dissipation due to upwind discretization, which is evident from the numerical test examples.

Upwind treatment of only the convective part of the inviscid flux terms, instead of the whole inviscid flux term, leads to more accurate solutions even at relatively coarse grids, which is substantiated by numerical test examples.

The method is presently applicable to Cartesian grid.

Although similar formulation is reported by Vierendeels et al., no detailed study of the accuracy is presented. Discretization and solution reconstructions used in the present approach differ from the approach reported by Vierendeels et al. A modification to Vierendeels type scheme is proposed that can help in achieving divergence free velocity condition. Finally the efficacy of the present approach to produce very accurate solutions even on coarse grids is successfully demonstrated using a few benchmark problems.

The purpose of this paper is to develop a combined method for three-dimensional incompressible flow and heat transfer by the spectral collocation method (SCM) and the artificial compressibility method (ACM), and further to study the performance of the combined method SCM-ACM for three-dimensional incompressible flow and heat transfer.

The partial differentials in space are discretized by the SCM with Chebyshev polynomial and Chebyshev–Gauss–Lobbatto collocation points. The unsteady artificial compressibility equations are solved to obtain the steady results by the ACM. Three-dimensional exact solutions with trigonometric function form and exponential function form are constructed to test the accuracy of the combined method.

The SCM-ACM is developed successfully for three-dimensional incompressible flow and heat transfer with high accuracy that the minimum value of variance can reach. The accuracy increases exponentially along with time marching steps. The accuracy is also improved exponentially with the increasing of nodes before stable accuracy is achieved, while it keeps stably with the increasing of the time step. The central processing unit time increases exponentially with the increasing of nodes and decreasing of the time step.

It is difficult for the implementation of the implicit scheme by the developed SCM-ACM. The SCM-ACM can be used for solving unsteady impressible fluid flow and heat transfer.

The SCM-ACM is applied for two classic cases of lid-driven cavity flow and natural convection in cubic cavities. The present results show good agreement with the published results with much fewer nodes.

The combined method SCM-ACM is developed, firstly, for solving three-dimensional incompressible fluid flow and heat transfer by the SCM and ACM. The performance of SCM-ACM is investigated. This combined method provides a new choice for solving three-dimensional fluid flow and heat transfer with high accuracy.

A new approach for solving steady incompressible Navier‐Stokes equations is presented in this paper. This method extends the upwind Riemann‐problem‐based techniques to viscous flows, which is obtained by applying modified artificial compressibility Navier‐Stokes equations and fully discrete high‐order numerical schemes for systems of advection‐diffusion equations. In this approach, utilizing the local Riemann solutions the steady incompressible viscous flows can be solved in a similar way to that of inviscid hyperbolic conservation laws. Numerical experiments on the driven cavity problem indicate that this approach can give satisfactory solutions.

The purpose of this paper is the development of a new density-based (DB) semi-Lagrangian method to speed up the conventional pressure-based (PB) semi-Lagrangian methods.

The semi-Lagrangian-based solvers are typically PB, i.e. semi-Lagrangian pressure-based (SLPB) solvers, where a Poisson equation is solved for obtaining the pressure field and ensuring a divergence-free flow field. As an elliptic-type equation, the Poisson equation often relies on an iterative solution, so it can create a challenge of parallel computing and a bottleneck of computing speed. This study proposes a new DB semi-Lagrangian method, i.e. the semi-Lagrangian artificial compressibility (SLAC), which replaces the Poisson equation by a hyperbolic continuity equation with an added artificial compressibility (AC) term, so a time-marching solution is possible. Without the Poisson equation, the proposed SLAC solver is faster, particularly for the cases with more computational cells, and better suited for parallel computing.

The study compares the accuracy and the computing speeds of both SLPB and SLAC solvers for the lid-driven cavity flow and the step-flow problems. It shows that the proposed SLAC solver is able to achieve the same results as the SLPB, whereas with a 3.03 times speed up before using the OpenMP parallelization and a 3.35 times speed up for the large grid number case (512 × 512) after the parallelization. The speed up can be improved further for larger cases because of increasing the condition number of the coefficient matrixes of the Poisson equation.

This paper proposes a method of avoiding solving the Poisson equation, a typical computing bottleneck for semi-Lagrangian-based fluid solvers by converting the conventional PB solver (SLPB) to the DB solver (SLAC) through the addition of the AC term. The method simplifies and facilitates the parallelization process of semi-Lagrangian-based fluid solvers for modern HPC infrastructures, such as OpenMP and GPU computing.

This study aims to feature the application of the artificial compressibility method (ACM) for the numerical prediction of two-dimensional (2D) axisymmetric swirling flows.

The respective academic numerical solver, named IGal2D, is based on the axisymmetric Reynolds-averaged Navier–Stokes (RANS) equations, arranged in a pseudo-Cartesian form, enhanced by the addition of the circumferential momentum equation. Discretization of spatial derivative terms within the governing equations is performed via unstructured 2D grid layouts, with a node-centered finite-volume scheme. For the evaluation of inviscid fluxes, the upwind Roe’s approximate Riemann solver is applied, coupled with a higher-order accurate spatial reconstruction, whereas an element-based approach is used for the calculation of gradients required for the viscous ones. Time integration is succeeded through a second-order accurate four-stage Runge-Kutta method, adopting additionally a local time-stepping technique. Further acceleration, in terms of computational time, is achieved by using an agglomeration multigrid scheme, incorporating the full approximation scheme in a V-cycle process, within an efficient edge-based data structure.

A detailed validation of the proposed numerical methodology is performed by encountering both inviscid and viscous (laminar and turbulent) swirling flows with axial symmetry. IGal2D is compared against the commercial software ANSYS fluent – by using appropriate metrics and characteristic flow quantities – but also against experimental measurements, confirming the proposed methodology’s potential to predict such flows in terms of accuracy.

This study provides a robust methodology for the accurate prediction of swirling flows by combining the axisymmetric RANS equations with ACM. In addition, a detailed description of the convective flux Jacobian is provided, filling a respective gap in research literature.

The purpose of this paper is to present numerical study on the behaviour of 2D unsteady incompressible laminar wakes behind square cylinders.

The numerical method that has been developed is based on a finite point formulation characterised by its weak connectivity requirements. This formulation allows for a patched unstructured approach to computational domain modelling that is of interest for industrial applications. Time evolution of pressure is computed by using a pseudo‐compressibility relaxation model that is based on physical considerations.

This model is characterised by the fact that no sub‐iterations on a numerical pseudo‐time are required so that computational efficiency is increased. Algorithm stability requires the use of second and fourth order artificial viscosity operators that effectively change the order of the equations. A discussion is included regarding the boundary conditions for these operators that do not influence vortex shedding behaviour.

Bearing in mind the industrial drive (MEMS design) that the authors have in mind, solver validation has been addressed at two levels: global coefficients (lift, drag and Strouhal number) were compared with those published in the specialised literature, while local velocity and rms profiles were compared with those obtained after performing a specific low velocity wind tunnel testing campaign (Reynolds numbers in the range from 110 to 268).

A sensitivity analysis of the results obtained is presented and it shows that the solver numerical robustness makes it amenable for project oriented applications.

The formulation being presented is competitive and could be considered as a potential alternative to other approaches.

The purpose of the paper is to numerically simulate steady‐state thermo‐solutal convection in rectangular cavities with different aspect ratios, subject to horizontal temperature and concentration gradients, and validate the results against numerical and experimental data available from literature.

The fully explicit Artificial Compressibility (AC) version of the Characteristic Based Split (CBS) scheme is adopted to solve double diffusion (DD) problems. A stabilization analysis is carried out to efficiently solve the problems considered in the present work. The thermal and solutal buoyancy forces acting on the fluid have been taken into account in case of aiding and opposing flow conditions.

The stability limits derived by the authors for the thermo‐solutal convection assume a fundamental role to efficiently solve the DD problems considered. In the cases characterized by higher Rayleigh number the convergent solution is obtained only by employing the new stability conditions. The efficient matrix free procedure employed is a powerful tool to study complex DD problems.

In this paper, the authors extend the stabilization analysis for the AC‐CBS scheme to the solution of DD, fundamental to efficiently solve the present problems, and apply the present fully explicit matrix free scheme, based on finite elements, to the solution of DD natural convection in cavities.

The purpose of this paper is to present a numerical method for the simulation of steady and unsteady incompressible laminar flows, including convective heat transfer.

A node centered, finite volume discretization technique is applied on hybrid meshes. The developed solver, is based on the artificial compressibility approach.

A sufficient number of representative test cases have been examined for the validation of this numerical solver. A wide range of the various dimensionless parameters were applied for different working fluids, in order to estimate the general applicability of our solver. The obtained results agree well with those published by other researchers. The strongly coupled solution of the governing equations showed superiority compared to the loosely coupled solution as inviscid effects increase.

Convective heat transfer is dominant in a wide variety of practical engineering problems, such as cooling of electronic chips, design of heat exchangers and fire simulation and suspension in tunnels.

A comparison between the strongly coupled solution and the loosely coupled solution of the Navier-Stokes and energy equations is presented. A robust upwind scheme based on Roe’s approximate Riemann solver is proposed.

This study is concerned with developing laminar flow of an incompressible, Newtonian fluid, having constant viscosity, rotating in circular and rectangular ducts that contain a 180° bend. The Reynolds number ranges from 100 to 400, the rotation number from 0 to 0.4, and the Dean number from 66 to 264. Positive and negative rotation modes are considered. The artificial compressibility method is used for the numerical calculations and new boundary conditions are developed for these flows. It is shown that rotation causes the secondary flow to occur in ducts of any geometry, and that the strength of the secondary flow in the bend due to both rotation and curvature decreases as compared to the no rotation case.